# Find the position function if the acceleration function is a(t) = 10 \sin(t) + 1 , the initial...

## Question:

Find the position function if the acceleration function is {eq}a(t) = 10 \sin(t) + 1 {/eq}, the initial velocity is {eq}v(0) = -7 {/eq} and the initial position is {eq}s(0) = 6 {/eq}.

## Motion:

Any movement can be described in terms of three variables: position, velocity, and acceleration. The velocity of an object is defined as the change in its position over a given time interval. In turn, the acceleration is the change in velocity over time. We can relate these three parameters together through differentiation and integration.

## Answer and Explanation: 1

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Given the acceleration function:

{eq}\displaystyle \rm a(t) = 10\sin\ t + 1 {/eq}

To get the velocity function, we can integrate this:

{eq}\disp...

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Chapter 14 / Lesson 1The integral of velocity with respect to time can be calculated to find the current position of a person or object. In this lesson, take a closer look at the concept of dynamic motion and explore how to solve it using integration.

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